Can anyone help me with this math problem?

Question

I'm in summer school and I was wondering if anyone could answer this.

Solve the system.

5x – 2y = 4

4x – y = 5

this is just a random problem, the answer isn't what I need I was just wondering if anyone could show me how to work these types of problems out.

Answer 1

on a graph or simultaneously?

simultaneously; you want to be able to add the two equations together so that one variable gets cancelled out.  Notice how if we multiply the second equation by -2, we get -2y and 2y which makes zero leaving us with just x to solve for.

5x – 2y = 4

-2 * [4x – y = 5] = -8x + 2y = -10

Add the two equations

5x – 2y = 4

-8x + 2y = -10

-3x = -6

x = 2

Use x in any of the two equations to solve for y

4x – y = 5, if x = 2

4(2) - y = 5

8 - y = 5

8 - 5 = y

3 = y

solution (2, 3)

If you wanted to do it graphically you would solve for y in terms of x and graph the lines to see where they intersect.

5x - 2y = 4 --> (5x - 4)/2 = y or y = 5/2 x - 2

4x - y = 5 --> y = 4x - 5

Answer 2

The first thing to do is solve one of the equations for one of the variables.

Lets take the second one:

4X - Y = 5

adding Y to both sides

4X = 5 + Y

subtracting 5 from both sides

4X - 5 = Y

Now since 4X - 5 is the same as Y let's substitute it for Y in the other equation:

5X - 2(4X - 5) = 4

multiply the term in the parens

5X - 8X + 10 = 4

subtract 10 from both sides

5X - 8X = -6

reduce

-3X = -6

multiply both sides by -1

3X = 6

divide both sides by 3

X = 2

Now substitute X into Y=4X-5

Y = 4*2 - 5

Y = 3

So X = 2 and Y = 3

Insert these values into the original equations to verify

5*2 - 2*3 = 4

10 - 6 = 4

and

4*2 - 3 = 5

8 - 3 =5

Answer 3

this is a substitution problem

take 4x-y=5

       y=4x-5

now take 5x - 2y =4

substitute the value of y

  5x - 2(4x -5)=4

  5x - 8x +10= 4

  -3x = -6

  x=2